Did a goggle search and see that sealant is the preferred method...Can I can do for alot less than $4K or do I have to have a licensed constractor do this?

The sealant is expensive too.

I would think some type of sealant on the inside walls and a good de-humidifier along with double checking the downspouts on the house would be sufficient. 

Should I put some sealant(I think that's what it's called) on the crack.

I would also look for popped nails, and and exposed nails on penetrations, where the sealant is gone away.

My contractor tells me the sealant is very expensive.

Part of the reason we couldn't agree on price was that we were making the assumption that more sheetrock needed to come out and more containment (appropriate paint sealant) needed to be done to the exposed structure.

If the gap is not affecting your property in anyways, you can just seal it up with a sealant.

Abatement or Remediation:  Many contractors will try to "sell you" on encapsulation, which is acceptable, (such as "painting it" with a recognized/certified sealant)  but leaves the potential there... and again it is ALL about disclosure...Abatement/Remediation is the more costly but permanent solution.... if is a roof, the roofer should be certified in the removal and disposal.

Something like this:   http://www.amazon.com/gp/product/B002RT7BH2/They also have similar items at lowes/home depot.As far as the sealant on the tub/shower...why was that installed?